IMPROVING THE UNIVERSITY'S PERFORMANCE IN PUBLIC POLICY EDUCATION

Teaching/Communication/Extension/Profession,

Rectification of a whole-sky photograph as a tool for determining spatial positioning of cumulus clouds

There are no author-identified significant results in this report

Sharp Oracle Inequalities for Square Root Regularization

We study a set of regularization methods for high-dimensional linear regression models. These penalized estimators have the square root of the residual sum of squared errors as loss function, and any weakly decomposable norm as penalty function. This fit measure is chosen because of its property that the estimator does not depend on the unknown standard deviation of the noise. On the other hand, a generalized weakly decomposable norm penalty is very useful in being able to deal with different underlying sparsity structures. We can choose a different sparsity inducing norm depending on how we want to interpret the unknown parameter vector $\beta$. Structured sparsity norms, as defined in Micchelli et al. [18], are special cases of weakly decomposable norms, therefore we also include the square root LASSO (Belloni et al. [3]), the group square root LASSO (Bunea et al. [10]) and a new method called the square root SLOPE (in a similar fashion to the SLOPE from Bogdan et al. [6]). For this collection of estimators our results provide sharp oracle inequalities with the Karush-Kuhn-Tucker conditions. We discuss some examples of estimators. Based on a simulation we illustrate some advantages of the square root SLOPE

χ2\chi^2-confidence sets in high-dimensional regression

We study a high-dimensional regression model. Aim is to construct a confidence set for a given group of regression coefficients, treating all other regression coefficients as nuisance parameters. We apply a one-step procedure with the square-root Lasso as initial estimator and a multivariate square-root Lasso for constructing a surrogate Fisher information matrix. The multivariate square-root Lasso is based on nuclear norm loss with $\ell_1$-penalty. We show that this procedure leads to an asymptotically $\chi^2$-distributed pivot, with a remainder term depending only on the $\ell_1$-error of the initial estimator. We show that under $\ell_1$-sparsity conditions on the regression coefficients $\beta^0$ the square-root Lasso produces to a consistent estimator of the noise variance and we establish sharp oracle inequalities which show that the remainder term is small under further sparsity conditions on $\beta^0$ and compatibility conditions on the design.Comment: 22 page

A remark on nets of threshold elements

The necessary condition for transition functions of Simple McCulloch-Pitts Nets, given in the article: “Nets of Threshold Elements≓ by Kenneth Krohn and John Rhodes in Corollary 3.1. (iii) is enlarged to a sufficient criterion by addition of another necessary condition

Morphology, Bioacoustics, and Ecology of Tibicen neomexicensis sp. n., a New Species of cicada from the Sacramento Mountains in New Mexico, U.S.A. (Hemiptera, Cicadidae, Tibicen)

Tibicen neomexicensis sp. n., a new species of cicada found in the Sacramento Mountains of southcentral New Mexico, is described. T. neomexicensis closely resembles T. chiricahua Davis morphologically, but males of the two species have highly distinct calling songs that differ in phrasal structure, amplitude burst rates, and pulse structure. Unlike T. chiricahua, male T. neomexicensis use conspicuous dorso-ventral abdominal movements to modulate the amplitude and frequency of their calls. T. neomexicensis is also smaller on average than T. chiricahua, and differences in the color patterns of the wing venation identify these two species morphologically. Both species are dependent on pinyon-juniper woodlands and have similar emergence phenologies. These species appear to be allopatric, with T. chiricahua found west of the Rio Grande in New Mexico, Arizona, and Mexico, and T. neomexicensis so far known only from New Mexico, east of the Rio Grande. T. chiricahua and T. neomexicensis males share a common genitalic structure that separates them from all other species of Tibicen, and the possible evolutionary and biogeographic history of these likely sister species is also discussed

A Proposal to Enhance Mentoring at SPEA IUPUI

Short talk presentation slide